A cooling device or spraying nozzle assembly of the type set out in the introduction is known. For example, the company Sulzer Metco provides for cold gas spraying under the protected trade name “Kinetics 4000 Cold Spray Gun” a spraying nozzle assembly in which the spraying nozzle is surrounded by a pipe. Between the spraying nozzle and the pipe, there is produced an annular gap through which it is possible to direct cooling air which flows from an inlet in the converging portion of the nozzle to an outlet at the nozzle mouth. The cooling air in this instance passes directly over the outer side of the spray nozzle, wherein the absorption capacity of the gaseous cooling medium for the heat discharged from the spraying nozzle is comparatively limited.